/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q26MP 鈭琕脳苍诲蟽聽聽over the entire su... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q26MP (page 338)

鈭�V脳苍诲蟽over the entire surface of the cube in the first octant with three faces in the three coordinate planes and the other three faces intersecting at (2,2,2), where V=(2鈭�y)i+xzj+xyzk.

Short Answer

Expert verified

The Solution is鈭�鈭�T鈥�(鈭�脳V)脳苍诲蟽=0.

Step by step solution

01

Given Information.

The given information is,V=(2鈭�y)i+xzj+xyzk

02

Definition of Divergence Theorem.

The divergence theorem, often known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

03

Find the solution.

Use the divergence theorem 鈭�T鈥�鈭�脳VdT=鈭�鈭�T鈥�V脳苍诲蟽, where is the surface area that encloses the volume T.

鈭�脳(鈭�脳V)=0

But the divergence of any curve is zero. Use the triplet scale product.

鈭�鈭�T鈥�(鈭�脳V)脳苍诲蟽=鈭�J鈥�鈭�脳(鈭�脳V)dT

=0

Hence, the solution is 鈭�鈭�T鈥�(鈭�脳V)脳苍诲蟽=0.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The force F = i - 2jacts at the point (0, 1, 2) Find the torque of F about the line =(2i-j)t.

Evaluate each of the integrals in Problems 3 to 8 as either a volume integral or a surface integral, whichever is easier.

鈭�V-苍诲蟽ifV=xcos2yi+xzj+zsin2ykover the surface of a sphere with center at the origin and radius 3.

Evaluatethelineintegral鈭�(x2-y2)dx-2xydyalongeachofthefollowingpathsfrom(0,0)to(1,2).(a)y=2x2.(b)x=t2(c)y=0fromx=0tox=2;thenalongthestraightlinejoining(2,0)to(1,2).

Find the total work done by forces and if the object undergoes the displacement C . Hint: Can you add the two forces first?

Show thatF=y2zsinh鈦�(2xz)i+2ycosh2鈦�(xz)j+y2xsinh鈦�(2xz)k is conservative, and find a scalar potential 蠁such that F=鈭�鈭�蠒.
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Translational Dynamics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Fundamentals of Physics

Read Explanation

Dynamics

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.